Abstract
Practices that fall under the broad umbrella of ‘computation’ in the western European Middle Ages tend to be goal-oriented and directed at specific purposes, such as the computation of the date of Easter, the calculation of velocities, and the combinatorics of syllogisms and other logical arguments. In spite of this practical bent, disparate computational practices were increasingly built upon theoretical foundations. In this chapter, we discuss the theoretical principles underlying three areas of computation: computistics and the algorithms employed in computistics, as well as algorithms more generally; arithmetic and mathematical calculation, including the calculation of physical facts and theorems; and (possible) physical implementations of computing mechanisms.
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Because many of them were associated with Merton College, they are often also known as the ‘Merton Calculators’; but because not all were members of Merton, this is not an optimal label.
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Kilvington is often cited as the first of the Calculators; however, his methods differed from that of later calculators (Kretzmann 1988, p. 226; Ashworth 1992, p. 520), and it is likely that he left Oxford before the others Calculators really became active (Sylla 1999). Nevertheless, his treatises were enormously influential on the later Calculators, especially on William Heytesbury, student of Kilvington, whose Regule solvendi sophismata (1335) is indebted to Kilvington’s Sophismata (Wilson 1956, p. 7).
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The Kneales do not say who these “some people” are, and I have had no success in determining this.
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For biographical information, see Llull and Bonner (1985, vol. 1, pp. 3–52), which includes extensive excerpts from Llull’s autobiography.
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The diagrams of the first, second, third, and fourth figures of the Ars brevis as found in the Escorial MS are reproduced in Llull and Bonner (1985) between pages 582 and 583.
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Uckelman, S.L. (2018). Computation in Medieval Western Europe. In: Hansson, S. (eds) Technology and Mathematics. Philosophy of Engineering and Technology, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-93779-3_3
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